Hard Math Question!

The owner os a small Nutt's & Nuts company makes and sells two types of 5-ounce mixed nuts packages. A low-grade mixture containing 3 ounces of cashews and 2 ounces of peanuts and a high-grade mixture containing 4 ounces of cashews and 1 ounce of peanuts. The profit is $.70 on each package of the low-grade mixture and $.80 on each package of the high-grade mixture. The mixing machine that gets filled every hour can hold utmost 36 ounces of cashews and no more than 14 ounces of peanuts. By graphing, find: a) the maximum hourly profit, and b) the production schedule that maximizes the hourly profit.

A company makes and sells two types of 5-ounce mixed nuts packages.
A low-grade mixture containing 3 ounces of cashews and 2 ounces of peanuts
and a high-grade mixture containing 4 ounces of cashews and 1 ounce of peanuts.

The profit is $0.70 on each package of the low-grade mixture
and $0.80 on each package of the high-grade mixture.

The mixing machine that gets filled every hour can hold at most 36 ounces of cashews
and no more than 14 ounces of peanuts.

By graphing, find:
a) the maximum hourly profit
b) the production schedule that maximizes the hourly profit.Why do they always ask these questions backwards ??

Organize the data . . .

. .

We have: .

Profit Function: .

[1] and [2] places us in Quadrant 1.

The line of [3] is: .. . It has intercepts (12,0) and (0,9).. . Graph the line and shade the region below the line.

The line of [4] is: .. . It has intercepts (7,0) and (0,14).. . Graph the line and shade the region below the line.